Dependencies of micro-pillar cavity quality factors calculated with finite element methods

Optics Express

Volumn 17, Issue 2, 2009, Pages 1144-1158

  Karl, M ^a   Kettner, B ^b   Burger, S ^b   Schmidt, F ^b   Kalt, H ^a   Hetterich, M ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

OPTICAL CONSTANTS; OPTICS;

CAVITY QUALITY FACTOR; CRITICAL FEATURES; FUNDAMENTAL MODES; LIGHT CONFINEMENTS; OPTICAL MODES; PILLAR DIAMETERS; QUALITY FACTORS; SEMICONDUCTOR CAVITY;

FINITE ELEMENT METHOD;

EID: 58449098124     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.17.001144     Document Type: Article

References (35)

1. E. M. Purcell, "Spontaneous emission probabilities at radio frequencies," Phys. Rev. 69, 681 (1946).
2. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
3. J. P. Reithmaier, G. Sȩk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dotsemiconductor microcavity system," Nature (London) 432, 197-200 (2004).
4. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature (London) 432, 200-203 (2004).
5. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, "A Quantum Dot Single-Photon Turnstile Device," Science 290, 2282-2285 (2000).
6. A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, "Quantum Information Processing Using Quantum Dot Spins and Cavity QED," Phys. Rev. Lett. 83, 4204-4207 (1999).
7. G. Ortner, M. Bayer, Y. Lyanda-Geller, T. L. Reinecke, A. Kress, J. P. Reithmaier, and A. Forchel, "Control of Vertically Coupled InGaAs/GaAs Quantum Dots with Electric Fields," Phys. Rev. Lett. 94, 157401 (2005).
8. M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, "Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances," Phys. Rev. B 77, 035108 (2008).
9. M. Karl, S. Li, T. Passow, W. Löffler, H. Kalt, and M. Hetterich, "Localized and delocalized modes in coupled optical micropillar cavities," Opt. Express 15, 8191-8196 (2007).
10. K. Srinivasan, M. Borselli, T. J. Johnson, P. E. Barclay, O. Painter, A. Stintz, and S. Krishna, "Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots," Appl. Phys. Lett. 86, 151106 (2005).
11. F. M. Weber, M. Karl, J. Lupaca-Schomber, W. Löffler, S. Li, T. Passow, J. Hawecker, D. Gerthsen, H. Kalt, and M. Hetterich, "Optical modes in pyramidal GaAs microcavities," Appl. Phys. Lett. 90, 161104 (2007).
12. M. Karl, T. Beck, S. Li, H. Kalt, and M. Hetterich, "Q-factor and density of optical modes in pyramidal and cone-shaped GaAs microcavities," Appl. Phys. Lett. 92, 231105 (2008).
13. S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauss, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, "AlAs/GaAs micropillar cavities with quality factors exceeding 150.000," Appl. Phys. Lett. 90, 251109 (2007).
14. A. J. Bennett, D. J. P. Ellis, A. J. Shields, P. Atkinson, I. Farrer, and D. A. Ritchie, "Observation of the Purcell effect in high-index-contrast micropillars," Appl. Phys. Lett. 90, 191911 (2007).
15. J. Vučković, M. Pelton, A. Scherer, and Y. Yamamoto "Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics," Phys. Rev. A 66, 023808 (2002).
16. Y.-L. D. Ho, T. Cao, P. S. Ivanov, M. J. Cryan, I. J. Craddock, C. J. Railton, and J. G. Rarity "Three-Dimensional FDTD Simulation of Micro-Pillar Microcavity Geometries Suitable for Efficient Single-Photon Sources," IEEE J. Quantum Electron. 43, 462-472 (2007).
17. N. Gregersen, T. R. Nielsen, B. Tromborg, and J. Mørk, "Quality factors of nonideal micro pillars," Appl. Phys. Lett. 91, 011116 (2007).
18. Ph. Lalanne, J. P. Hugonin, and J. M Gérard, "Electromagnetic study of the quality factor of pillar microcavities in the small diameter limit," Appl. Phys. Lett. 84, 4726-4728 (2004).
19. G. Lecamp, J. P. Hugonin, P. Lalanne, R. Braive, S. Varoutsis, S. Laurent, A. Lemaître, I. Sagnes, G. Patriarche, I. Robert-Philip, and I. Abram, "Submicron-diameter semiconductor pillar microcavities with very high quality factors," Appl. Phys. Lett. 90, 091120 (2007).
20. J. Pomplun, S. Burger, L. Zschiedrich and F. Schmidt, "Adaptive Finite Element Method for Simulation of Optical Nano Structures," Phys. Status Solidi B, 244, 3419-3434 (2007).
21. L. Zschiedrich, R. Klose, A. Schädle and F. Schmidt "A new finite element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D," J. Comput Appl. Math., 188, 12-32, (2006).
22. L. Zschiedrich, S. Burger, B. Kettner, and F. Schmidt , "Advanced Finite Element Method for Nano Resonators," in Physics and Simulation of Optoelectronic Devices XIV M. Osinski, F. Henneberger, and Y. Arakawa, eds. SPIE 6115, 164-174 (2006).
23. S. Burger, R. Kohle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, C. Nölscher "Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation," Proc. SPIE 5992, 378-289 (2005).
24. J. L. Jewell, S. L. McCall, A. Scherer, H. H. Houh, N. A. Whitaker, A. C. Gossard, and J. H. English, "Transverse modes, waveguide dispersion, and 30 ps recovery in submicron GaAs/AlAs microresonators," Appl. Phys. Lett. 55, 22-24 (1989).
25. J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera , "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
26. M. Benyoucef, S. M. Ulrich, P. Michler, J. Wiersig, F. Jahnke, and A. Forchel, "Correlated photon pairs from single (In,Ga)As/GaAs quantum dots in pillar microcavities," J. Appl. Phys. 97, 023101 (2005).
27. 1-xAs alloys system," J. Appl. Phys. 47, 2604-2613 (1976).
28. 1-xAs double heterostructures," J. Appl. Phys. 45, 800-807 (1974).
29. M. D. Sturge, "Optical Absorption of Gallium Arsenide between 0.6 and 2.75 eV," Phys. Rev. 127, 768-773 (1962).
30. WVase32, J.A. Woollam Co. Inc., Lincoln, USA.
31. G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, A. Scherer, "Vacuum Rabi splitting in semiconductors," Nature Physics 2, 81-90 (2006).
32. J. Hendrickson, B. C. Richards, J. Sweet, S. Mosor, C. Christenson, D. Lam, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, "Quantum dot photonic-crystalslab nanocavities: Quality factors and lasing," Phys. Rev. B 72, 193303 (2005).
33. T. Tawara, H. Kamada, Y.-H. Zhang, T. Tanabe, N. I. Cade, H. Gotoh, D. Ding, S. R. Johnson, E. Kuramochi, M. Notomi, and H. Nakano, "Role of Re-absorption Effect to Quality Factor in Quantum-Dot Photonic-Crystal Nanocavities," in Proceedings of IEEE International Conference. on Indium Phosphide and Related Materials (Institute of Electrical and Electronics Engineers, New York, 2007), pp. 490-492.
34. M. Benyoucef, S.M. Ulrich, P. Michler, J. Wiersig, F. Jahnke and A. Forchel, "Enhanced correlated photon pair emission from a pillar microcavity," New J. Phys. 6, 91 (2004).
35. J. M. Gérard, B. Sermarge, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, "Enhanced Spontaneous Emission by Quantum Boxes in a Monolithic Optical Microcavity," Phys. Rev. Lett. 81, 1110-1113 (1998).